On evolution algebras

By J. M. Casas, Manuel Ladra, Bakhrom Omirov, Utkir A. Rozikov. 2010

87 citations recorded by the source corpus.

The structural constants of an evolution algebra is given by a quadratic matrix $A$. In this work we establish equivalence between nil, right nilpotent evolution algebras and evolution algebras, which are defined by upper triangular matrix $A$. The classification of 2-dimensional complex evolution algebras is obtained. For an evolution algebra with a special form of the matrix $A$ we describe all its isomorphisms and their compositions. We construct an algorithm running under Mathematica which decides if two finite dimensional evolution algebras are isomorphic.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/690ab9d177aec5b3dcff6d235fbc0c76ce07039d

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In Algebra and Number Theory

1. Yolanda Cabrera Casado
2. M. V. Velasco
3. Mercedes Siles Molina
4. G. Pino

In Geometry and Topology

1. Yolanda Cabrera Casado
2. M. V. Velasco
3. Mercedes Siles Molina
4. G. Pino

Citations in the corpus

• Evolution algebras of arbitrary dimension and their decompositions (2016, background): “Algebraic notions as nilpotency and solvability may be interpreted biologically as the fact that some of the original gametes (or generators) become extinct after a certain number of generations, and these algebraic properties have been studied in [6, 4, 20, 24, 7, 13, 9].”